The differential-geometric and topological structure of Delsarte transmutation operators and their associated Gelfand-Levitan-Marchenko type eqautions are studied along with classical Dirac type operator and its multidimensional affine extension, related with selfdual Yang-Mills eqautions. The construction of soliton-like solutions to the related set of nonlinear dynamical system is discussed.
@article{bwmeta1.element.doi-10_2478_BF02475922,
author = {Anatoliy Samoilenko and Yarema Prykarpatsky and Anatoliy Prykarpatsky},
title = {The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {529-557},
zbl = {1114.34007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475922}
}
Anatoliy Samoilenko; Yarema Prykarpatsky; Anatoliy Prykarpatsky. The generalized de Rham-Hodge theory aspects of Delsarte-Darboux type transformations in multidimension. Open Mathematics, Tome 3 (2005) pp. 529-557. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475922/
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